Tough government follow-through on a freshly minted U.S. financial law will be crucial to ensure no bank or firm grows so large that its collapse could jeopardize the entire economy, Federal Reserve Chairman Ben Bernanke said on Thursday.

Bernanke and Federal Deposit Insurance Corp Chairman Sheila Bair said strong implementation of the new financial rules are essential to preventing a repeat of the recent economic melt-down that began in the United States and wreaked havoc around the world.

If the crisis has a single lesson, it is that the too-big-to-fail problem must be solved, the Fed chairman said in testimony prepared for delivery to the Financial Crisis Inquiry Commission.

Stricter capital and liquidity norms, a regime to wind down a failing firm in an orderly fashion, and requirements that most derivatives are to be settled in clearinghouses, will strengthen the financial system and help address the too-big-to-fail problem, Bernanke said.

Bair said the Dodd-Frank Act reduces the likelihood of future crises, and gives regulators the ability to handle failing financial giants without resorting to bailouts -- but only if the reforms are properly implemented.

She said the FDIC must have real-time data on financial firms' conditions. Firms and other regulators must also cooperate with the FDIC so it can do extensive advance planning.

If implementation is not properly carried out, the reforms could be ineffective in preventing future crises or containing financial market disruptions should they occur, she said in written testimony.

Bernanke pledged the Fed would increase enforcement actions where necessary and would deploy more-senior officials to engage bank officials on supervisory concerns in the future.

Reprising arguments he has made in the past, Bernanke said low interest rates in the early part of the decade cannot be blamed for the real estate bubble that exploded with such damaging consequences, instead pointing to relaxed lending standards and optimism fueled by rising prices.

Policymakers cannot rule out raising interest rates to slow an asset bubble from forming, but he said they should rely primarily on regulatory steps to slow excesses.

(Reporting by Mark Felsenthal; Editing by Tim Dobbyn)